Numerical Analysis of Steady State and Transient Motion of a Vibro-Impact System with Non-ideal Excitation with a Nonlinear Spring

Abstract

AbstractThis paper is studying the behaviour of a vibro-impact system with non-ideal excitation where the impacting oscillator is connected to a driving slider with a non-linear cubic spring. The paper is giving an insight in modelling and numerical analysis of steady state and transient motion of the system. The analysed system consists of an oscillating slider, a hard stop on one side of the oscillator, on the other side the oscillator is connected via a nonlinear spring to a slider. The driving slider is connected to a balanced disk with a link. The disk is attached to an electromotor shaft. The system is excited with a DC electromotor via the balanced disk. The electromotor characteristic is assumed to be linear and the mathematical model of it is shown in the paper. The impact model is inelastic. The equations of motions are derived using Lagrange’s equations. The numerical analysis is based on the continuation method of a run up and close down simulation by changing the stall torque value. Results are shown in the form of frequency response diagram, average value of the excitation frequency versus the stall torque value diagram and oscillation amplitude versus the stall torque value diagram for the steady state solutions. Based on these results transient motion is also analysed and results are shown in the form of diagrams which are describing the displacement and excitation frequency change in function of time. The aim of this paper is to show how the system behaves if the installed electromotor is weak or strong one. Through this analysis impact and non/impact solutions are obtained. It is pointed out that for which range of the stall torque values the system will have impact solutions or non-impact solutions. In reference to different regions the goal is to keep the system from the impact region assuming that the machine should just oscillate. The part of the paper where transient solutions are analysed is showing how the system can start as an vibro-impact system and switch to non-impact motion.KeywordsVibro-impact systemsNon-ideal excitationNonlinear springSteady state solutionsTransient solutionsNumerical analysis